We propose a new flexible distribution for data on the three-dimensional torus which we call a trivariate wrapped Cauchy copula. The proposed copula has the following advantages: (i) a simple form of density, (ii) an adjustable degree of dependence between every pair of variables, (iii) parameters with clear interpretation, (iv) well-known marginal and conditional distributions, (v) a straightforward data generating mechanism, (vi) unimodality, (vii) a closed-form expression for trigonometric moments, and (viii) a simple implementation procedure for obtaining maximum likelihood estimates. As is the case with general copula models, the proposed copula can be extended to have any specific marginal distributions and hence can be utilized for flexible modeling. Moreover, our construction allows for linear marginals, implying that our copula can also model cylindrical data, which consist of both angular and linear observations. As an application of the extended copula model on the three-dimensional torus, we consider a dataset of trivariate dihedral angles of amino acids in bioinformatics. Finally, we discuss how the proposed trivariate copula can be extended to multivariate copulas.
This is joint work with Christophe Ley (University of Luxembourg), Sophia Loizidou (University of Luxembourg), and Kanti V. Mardia (University of Leeds).
Zoom link: https://uoc-gr.zoom.us/j/88659969718?pwd=g6bjYPDCuUQo1bzVxjjbgQL4xFN1f3.1
